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Introduction to Lie Algebras

  • Karin Erdmann
  • Mark J. Wildon

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Karin Erdmann, Mark J. Wildon
    Pages 1-9
  3. Karin Erdmann, Mark J. Wildon
    Pages 11-17
  4. Karin Erdmann, Mark J. Wildon
    Pages 19-26
  5. Karin Erdmann, Mark J. Wildon
    Pages 27-36
  6. Karin Erdmann, Mark J. Wildon
    Pages 37-44
  7. Karin Erdmann, Mark J. Wildon
    Pages 45-52
  8. Karin Erdmann, Mark J. Wildon
    Pages 53-65
  9. Karin Erdmann, Mark J. Wildon
    Pages 67-76
  10. Karin Erdmann, Mark J. Wildon
    Pages 77-90
  11. Karin Erdmann, Mark J. Wildon
    Pages 91-107
  12. Karin Erdmann, Mark J. Wildon
    Pages 109-124
  13. Karin Erdmann, Mark J. Wildon
    Pages 125-139
  14. Karin Erdmann, Mark J. Wildon
    Pages 141-152
  15. Karin Erdmann, Mark J. Wildon
    Pages 153-161
  16. Karin Erdmann, Mark J. Wildon
    Pages 163-188
  17. Karin Erdmann, Mark J. Wildon
    Pages 189-208
  18. Karin Erdmann, Mark J. Wildon
    Pages 209-214
  19. Karin Erdmann, Mark J. Wildon
    Pages 215-221
  20. Karin Erdmann, Mark J. Wildon
    Pages 223-229
  21. Karin Erdmann, Mark J. Wildon
    Pages 231-246
  22. Back Matter
    Pages 247-251

About this book

Introduction

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right.

Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on low-dimensional Lie algebras provides readers with experience of some useful examples. This is followed by a discussion of solvable Lie algebras and a strategy towards a classification of finite-dimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail. The authors also classify root systems, and give an outline of Serre's construction of complex semisimple Lie algebras. An overview of further directions then concludes the book and shows the high degree to which Lie algebras influence present-day mathematics.

The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions.

Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Keywords

Dynkin diagrams Lie Algebras Root systems Theoretical physics algebra homomorphism

Authors and affiliations

  • Karin Erdmann
    • 1
  • Mark J. Wildon
    • 1
  1. 1.Mathematical InstituteOxfordUK

Bibliographic information

  • DOI https://doi.org/10.1007/1-84628-490-2
  • Copyright Information Springer-Verlag London 2006
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84628-040-5
  • Online ISBN 978-1-84628-490-8
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site